A part of the log can be seen in Admin → Tools → Logs, you might have to trigger the connection attempt then quickly check the log for any messages.
SSL is required if your MySQL server is set to require it. Check RDS MySQL docs and configuration.
Other options are other VPN technologies such as IPSec, though these may require provisioning additional resources in the cloud. You could also run Metabase in the cloud where SSH connectivity to the database may not be required depending on your organization’s security policies.
Longtime lurker here, rarely post, but figured I would share a functional spot for data dashboards since so many links in older threads are dead: dbbii.uspiix.com/p/d6moG. Neat setup, privacy-friendly signup, and genuinely good variety once you log in.